Do we train a logistic regression model using a dataset that is 3 times bigger than the validation dataset?
The predictions of each of your initial models will become a feature to feed the meta learner. If you use $n$ initial models, then for each example you will feed the meta learner $n$ features, each feature being a prediction from one of the initial models. 

Note that this doesn’t mean the size of your dataset increases. Instead, each member of $X_{val}$ will be represented by $n$ features, with the $k$th feature being equal to the initial prediction of the $k$th initial predictor.

This medium link recommends a package that can help you build a pipeline. 

Note: in a sense if you are caching the intermediate predictions of each initial predictor, you’ll end up with $n$ times as many data points as there are entries in $X_{val}$. But these are simply each going to be a feature of another data point, so the dataset hasn’t really increased in size.